Faces, Edges and Vertices worksheet
10 GCSE practice questions with answers, free to print. Every sheet is generated, so you can make a fresh one whenever you need it.
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3 marks
Think about a hexagonal prism.
(a)How many faces does it have?
(b)How many edges does it have?
(c)How many vertices does it have?
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3 marks
A traffic cone is a cone.
(A face is flat. A curved surface is not flat, so it is described separately. An edge is where two surfaces meet.)
(a)How many flat faces does it have?
(b)How many curved surfaces does it have?
(c)How many edges does it have?
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2 marks
A solid has \(7\) faces, \(12\) edges and \(7\) vertices, and six triangles meet at a point above a hexagon.
Write down the name of the solid.
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4 marks
Here is a cuboid. The dashed lines are the edges you cannot see from this side.
(a)State the number of faces.
(b)State the number of edges.
(c)State the number of vertices.
(d)Find the volume of the cuboid.
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5 marks
Here is a triangular prism.
(a)Write down the number of faces.
(b)Write down the number of edges.
(c)Write down the number of vertices.
(d)Calculate the volume of the prism.
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2 marks
A solid has \(12\) faces and \(30\) edges.
Euler's formula for a solid with flat faces is \(F + V - E = 2\).
Use it to work out how many vertices the solid has.
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3 marks
Think about a tetrahedron.
(a)How many faces does it have?
(b)How many edges does it have?
(c)How many vertices does it have?
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3 marks
A drinks can is a cylinder.
(A face is flat. A curved surface is not flat, so it is described separately. An edge is where two surfaces meet.)
(a)How many flat faces does it have?
(b)How many curved surfaces does it have?
(c)How many edges does it have?
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2 marks
A solid has \(7\) faces, \(15\) edges and \(10\) vertices, and two pentagons joined by five rectangles.
Write down the name of the solid.
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4 marks
The diagram shows a cuboid. The dashed lines are the edges you cannot see from this side.
(a)State the number of faces.
(b)State the number of edges.
(c)State the number of vertices.
(d)Work out the volume of the cuboid.
Answers
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(a) \(8\)
(b) \(18\)
(c) \(12\) -
(a) \(1\)
(b) \(1\)
(c) \(1\) - hexagonal pyramid
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(a) \(6\)
(b) \(12\)
(c) \(8\)
(d) \(108\ \text{cm³}\) -
(a) \(5\)
(b) \(9\)
(c) \(6\)
(d) \(270\ \text{cm³}\) - \(20\)
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(a) \(4\)
(b) \(6\)
(c) \(4\) -
(a) \(2\)
(b) \(1\)
(c) \(2\) - pentagonal prism
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(a) \(6\)
(b) \(12\)
(c) \(8\)
(d) \(108\ \text{cm³}\)